Garage Stereo

I have a garage stereo built off an Alpine deck and two amplifiers with 3 computer power supplies. Currently I turn off the power supplies when not in use to help them last longer. The problem with this is that all my presets and audio configuration gets erased every time. I need help designing something that will act as a backup power source so when I turn off my power supplies it will take over and provide enough power to store the presets. I have tried doing this with a relay and it didn’t switch fast enough I tried using a capacitor with the relay and still couldn’t get it to work.

What would you recommend doing to make this work? Would a simple diode inline with both circuits work so the power supplies don’t feed into each other? Will this hurt the deck? Did I possibly do something wrong with the capacitor to where it wouldn’t work? Also open to other ideas.

leave one of the computer power supplies on and run it into to constant power of the deck…or get a car battery too hook up to the constant power since the constant does not draw much current battery should still last a while